If you want a AMD64 3000+, 60 GB hard drive, 512 MB memory basic server,
two hour UPS, keyboard, scrollwheel mouse, etc ...
the e-machines M6805 laptop is available from best buy for $1100 or so
at the moment.

Does it have supported video?

Video is ATI 9600, which works fine (accelerated 2D, software 3D) using
the open source xfree86 drivers in 32 or 64 bit. The ATI binary driver,
that gives you accelerated 3D, was (last time I looked) only 32 bit and
the associated kernel module is not 64 bit capable. This may have changed.

I should point out, for people joining this thread, that this is an
Athlon64 not an Opteron laptop. We're using it as a compute server that
also controls lab experiments and has a built in X terminal. The
compute service has good availability because (even when an experiment
is being moved from one lab to another) the combination of battery and
wireless ensure that the other users can always talk to it. I'm
describing the display as an X terminal purely because of the lack of
accelerated 3D when in pure 64.

My wife bought a Compaq R3240ca for $1800cdn which is a 3200+ with 60G
512M, nvidia 440MX go video and 15.4 WXGA display and a DVD+RW drive and
(stupid hard to make work) broadcom 11g. Still have to get her to try
loading 64bit debian in addition to the 32bit.

Yeah, I'm using an external 802.11 card. The Nvidia video does, I
gather from this mailing list, run with the 32 bit libs in otherwise-pure64.